The method developed in [1]} uses QPE to extract the eigenvalues of the walk operator, which can then be related to the eigenvalues of the Hamiltonian.
This is the critical component from which we can develop a general procedure for solving matrix equations.
By treating a Hermitian system matrix as the Hamiltonian, we can apply QPE using the walk operator to extract the eigenvalues of the system matrix.
From there, the HHL algorithm can proceed as usual.
